Results 11 to 20 of about 63 (62)
Ideal extensions of ordered sets
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 53, Page 2847-2861, 2004., 2004 The ideal extensions of semigroups—without order—have been first considered by Clifford (1950). In this paper, we give the main theorem of the ideal extensions for ordered sets. If P, Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P′ which is isomorphic to P, and the complement of P′ in V is isomorphic to Q ...
Niovi Kehayopulu
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Extended blocker, deletion, and contraction maps on antichains
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 10, Page 607-616, 2003., 2003 Families of maps on the lattice of all antichains of a finite bounded poset that extend the blocker, deletion, and contraction maps on clutters are considered. Influence of the parameters of the maps is investigated. Order‐theoretic extensions of some principal relations for the set‐theoretic blocker, deletion, and contraction maps on clutters are ...
Andrey O. Matveev
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𝓜𝓝-convergence and lim-inf𝓜-convergence in partially ordered sets
Open Mathematics, 2018 In this paper, we first introduce the notion of 𝓜𝓝-convergence in posets as an unified form of O-convergence and O2-convergence. Then, by studying the fundamental properties of 𝓜𝓝-topology which is determined by 𝓜𝓝-convergence according to the standard ...
Sun Tao, Li Qingguo, Fan Nianbai
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A note on operators of deletion and contraction for antichains
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 12, Page 725-729, 2002., 2002 The operators of deletion and contraction for clutters are generalized to those for antichains of finite bounded posets. A generalization of the result by Seymour (1976), describing the relationship between the operators of deletion, contraction, and the blocker map, is considered as a comparison in the lattice of antichains of a poset.
Andrey O. Matveev
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Some results on ordered filters of implicative semigroups
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 12, Page 731-735, 2001., 2001 We introduce a special set in an implicative semigroup. Using it, an equivalent condition of an ordered filter is stated. We prove that an ordered filter can be represented by the union of such sets.
Young Bae Jun
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Some decompositions of filters in residuated lattices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this paper we introduce a new class of residuated lattice: residuated lattice with (C∧&→) property and we prove that (C∧&→) ⇔ (C→) + (C∧).Also, we introduce and characterize C→, C∨, C∧ and C∧ & → filters in residuated lattices (i.e., we characterize ...
Piciu Dana +2 more
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On ideals of implicative semigroups
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 2, Page 77-82, 2001., 2001 We introduce the notion of ideals in implicative semigroups, and then state the characterizations of the ideals.
Young Bae Jun, Kyung Ho Kim
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International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 10, Page 581-588, 2001., 2001 Antichains of a finite bounded poset are assigned antichains playing a role analogous to that played by blockers in the Boolean lattice of all subsets of a finite set. Some properties of lattices of generalized blockers are discussed.
Andrey O. Matveev
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Positive implicative ordered filters of implicative semigroups
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 12, Page 801-806, 2000., 2000 We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive implicative ordered filter.
Young Bae Jun, Kyung Ho Kim
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On chains and posets within the power set of a continuum
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 305-309, 1995., 1993 Transfinite induction is employed to construct a copy of an arbitrary partially‐ordered set of cardinality at most c within the power set (quasi‐ordered by sub‐chain embeddability) of the real line.
P. T. Matthews, T. B. M. McMaster
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